体积衍射光学元件的标量衍射数组分析
|
摘要
二元衍射光学元件由于其独特的性能及广泛的应用,有着传统光学元件无法比拟的优点,因此得以迅速发展。本文以体积衍射光栅为例,研究了二元衍射光学元件的夫朗和费衍射频谱面光强分布。
本文主要的方法为:由两束平面光(夹角为30°)干涉形成体积衍射光栅。将形成的光栅视为由很多薄光栅组成的厚光栅。由于是薄光栅,因此没有必要考虑布拉格效应,并将不同波长的衍射光,以不同的角度照射到体积衍射光栅上,模拟其夫朗和费衍射频谱面光强分布。本文研究的是位相型体积光栅。本文的研究内容为:
(1)在衍射光入射角为零度,波长为633nm时,随着厚度的增加,零级光越来越弱,一级光越来越强,直到厚度为36个薄片(即厚度为11394nm)时,光能量几乎完全分布在一级光的。这说明布拉格效应明显,同时也说明了我们的方法完全适用于体积衍射光栅。当厚度不足36个薄片(即厚度为11394nm)时,布拉格效应不明显,这是因为,此时的光栅,没有满足布拉格条件。改变衍射光入射波长为515nm或458nm,能得出同样的结论。
(2)在厚度均为40个薄片,不同波长时(458nm(厚度为9160nm))和(515nm(厚度为10300nm)),515nm的光几乎完全集中在一级光处,这满足布拉格条件。
(3)不同波长的衍射入射光,零级光出现的位置有变化,并且,随着波长的增加,一级光强随着波长的增加而增强。
(4)当以波长为633nm的衍射光以30°角入射时,随着厚度的增加,零级光逐渐变弱,一级光逐渐变强。当厚度为36(厚度为11394nm)个薄片时,衍射光几乎完全分布在一级光的位置。这说明,以干涉光角度入射时,也会发生布拉格效应。改变衍射光入射波长为515nm或458nm,能得出同样的结论。
Diffractive optical elements have special function and widely used, which has lots of merits that traditionally optics cannot analogy with,so it developed quickly. Take thick holographic gratings as examples, we studies Fraunhofer diffraction of diffractive optical elements.
We use two plane waves to interfere to produce a thick holographic grating. The method proceeds by decomposing the thick material into a series of thin slabs, each of which acts simply as a thin grating. Very general applicability can be obtained because all that need be specified are the properties of the thin gratings which may be absorption, phase or mixed. The contents of my paper are
(1)Angle of diffraction incidence is 0°,the wavelength is 633nm, with the increase of the thickness, zero order becomes weaker, the first order becomes stronger, till there are 36 thin slabs (i.e. the thickness is 11394nm ) ,light intensity is totally in the first order. This phenomenon obvious reflects Bragg Effect, because it satisfied the Bragg Law. If the wavelength is 515nm or 458nm, the same conclusion can be drawn.
(2)There are 40 thin slabs, the light of 515nm is totally in the first order. It satisfied the Bragg effact.
(3)Diffraction of incident light of different wavelengths, zero orders are in different places ,and with the increase of wavelengths,the first orders are stronger.
(4)Angle of diffraction incidence is 30°,with the increase of the thickness, the first order is stronger, till there are 36 thin slabs (i.e. the thickness is 11394nm ), light intensity is totally in the first order. This phenomenon obvious reflect Bragg Effect, it satisfy the Bragg Law. If the Wavelength is 515nm or 458nm, the same conclusion can be drawn. There are the same as the first results.
本文主要的方法为:由两束平面光(夹角为30°)干涉形成体积衍射光栅。将形成的光栅视为由很多薄光栅组成的厚光栅。由于是薄光栅,因此没有必要考虑布拉格效应,并将不同波长的衍射光,以不同的角度照射到体积衍射光栅上,模拟其夫朗和费衍射频谱面光强分布。本文研究的是位相型体积光栅。本文的研究内容为:
(1)在衍射光入射角为零度,波长为633nm时,随着厚度的增加,零级光越来越弱,一级光越来越强,直到厚度为36个薄片(即厚度为11394nm)时,光能量几乎完全分布在一级光的。这说明布拉格效应明显,同时也说明了我们的方法完全适用于体积衍射光栅。当厚度不足36个薄片(即厚度为11394nm)时,布拉格效应不明显,这是因为,此时的光栅,没有满足布拉格条件。改变衍射光入射波长为515nm或458nm,能得出同样的结论。
(2)在厚度均为40个薄片,不同波长时(458nm(厚度为9160nm))和(515nm(厚度为10300nm)),515nm的光几乎完全集中在一级光处,这满足布拉格条件。
(3)不同波长的衍射入射光,零级光出现的位置有变化,并且,随着波长的增加,一级光强随着波长的增加而增强。
(4)当以波长为633nm的衍射光以30°角入射时,随着厚度的增加,零级光逐渐变弱,一级光逐渐变强。当厚度为36(厚度为11394nm)个薄片时,衍射光几乎完全分布在一级光的位置。这说明,以干涉光角度入射时,也会发生布拉格效应。改变衍射光入射波长为515nm或458nm,能得出同样的结论。
Diffractive optical elements have special function and widely used, which has lots of merits that traditionally optics cannot analogy with,so it developed quickly. Take thick holographic gratings as examples, we studies Fraunhofer diffraction of diffractive optical elements.
We use two plane waves to interfere to produce a thick holographic grating. The method proceeds by decomposing the thick material into a series of thin slabs, each of which acts simply as a thin grating. Very general applicability can be obtained because all that need be specified are the properties of the thin gratings which may be absorption, phase or mixed. The contents of my paper are
(1)Angle of diffraction incidence is 0°,the wavelength is 633nm, with the increase of the thickness, zero order becomes weaker, the first order becomes stronger, till there are 36 thin slabs (i.e. the thickness is 11394nm ) ,light intensity is totally in the first order. This phenomenon obvious reflects Bragg Effect, because it satisfied the Bragg Law. If the wavelength is 515nm or 458nm, the same conclusion can be drawn.
(2)There are 40 thin slabs, the light of 515nm is totally in the first order. It satisfied the Bragg effact.
(3)Diffraction of incident light of different wavelengths, zero orders are in different places ,and with the increase of wavelengths,the first orders are stronger.
(4)Angle of diffraction incidence is 30°,with the increase of the thickness, the first order is stronger, till there are 36 thin slabs (i.e. the thickness is 11394nm ), light intensity is totally in the first order. This phenomenon obvious reflect Bragg Effect, it satisfy the Bragg Law. If the Wavelength is 515nm or 458nm, the same conclusion can be drawn. There are the same as the first results.
引文
[1] Gabor. A new microscopic principle.Nature.1948,161:777-778
[2] W. B. Veldkamp, T. J. McHugh. Binary Optics Scientific American.1992,266:92–97
[3]W. B.Veldkamp.Overview of Micro-optics:Past,Present,and Future. SPIE. 1991, 1544: 287–299
[4] J. Lcger, M.Holz, G.Swanson, W.B.Veldkamp. Coherent Laser Beam Addition:An Application of Binary Optics Technology. Lincoln Lab.J.1988,1(2):225–246
[5]金国藩,严瑛白,邬敏贤等著.二元光学.国防工业出版社,1998:9–12
[6] H.P.Herzig主编,周海宪等译.微光学元件、系统和应用.Taylor & Francis Ltd,1997:2–6
[7] J.R.Leger,M.G..Moharam,T.K. Gaylord. Diffractive Optics: An Introduction to the Feature Issue.Appl.Opt.1995,34(14):2399–2559
[8]J. A. Cox, M.G. Moharam, H. P. Herzig, J.N.Mait. Diffractive Optics and Micro-optics: Modeling, Design, Fabrication, and Applications.J.Opt.Soc..Am.A.1999,16(5):1093–1094
[9] J.M.Bendickson. Analysis of Finite Diffractive Optical Elements .Ph.D. thesis, Georgia Institute of Technology.2000
[10] J.Tervo.On Electromagnetic Treatment of Free-space Propagation and Paraxial Diffractive Optics. Ph.D. thesis, University of Joensuu.2002
[11] Y.Yirmiyahu, A.Niv,G.Biener, V.Kleiner,E.Hasman. Vectorial Vortex Mode Transformation for a Hollow Waveguide Using Pancharatnam -Berry Phase Optical Elements.Opt.Lett.2006,31(22):3252–3254
[12] G.Yang,B.Gu,X.Tan,M.Chang,B.Dong,O.K.Ersoy.Iterative Optimization Approach for the Design of Diffractive Phase Elements Simultaneously Implementing Several Optical Functions.J.Opt.Soc.Am.A.1994,11(5):1632-1640
[13] D.Feng,Y.Yan,G Jin,M.Wang.Rigorous Concept for the Analysis of Diffractive Lenses with Different Axial Resolution and High Lateral Resolution.Opt.Express.2003,11(17):1987–1994
[14] F.Di,Y.Yingbai,J.Guofan,T.Qiaofeng,H.Liu.Rigorous Electromagnetic Design of Finite-aperture Diffractive Optical Elements by Use of an Iterative Optimization Algorithm.J.Opt.Soc.Am.A.2003,20(9):1739–1746
[15] D.Feng,Y.Yan,G.Jin,S.Fan.Rigorous Electromagnetic Design of Finite aperture Diffractive Optical Elements by Use of an Iterative Optimization Algorithm.J.Opt.Soc.Am.A.2003,20(9):1739–1746
[16] S.-Q.Wang,J.Liu,B.-Y.Gu,Y.-Q.Wang,B.Hu,X.-D.Sun,S.Di.Rigorous Electromagnetic Analysis of the Common Focusing Characteristics of a Cylindrical Microlens with Long Focal Depth and under Multiwavelength Illumination.J.Opt.Soc.Am.A.2007,24(2):512–516
[17] J.Liu,B.-Y.Gu,B.-Z.Dong,G.-Z.Yang.Interference Effect of Dual Diffractive Cylindrical Microlenses Analyzed by Rigorous Electromagnetic Theory.J.Opt.Soc.Am.A.2001,18(3):526–536
[18] J.Liu,B.-Y.Gu.Laser Beam Shaping with Polarization-selective Diffractive PhaseElements.Appl.Opt.2000,39(18):3089–3092
[19] B.-Z.Dong,J.Liu,B.-Y.Gu,G.-Z.Yang,J.Wang.Rigorous Electromagnetic Analysis of a Microcylindrical Axilens with Long Focal Depth and High Transverse Resolution.J.Opt.Soc.Am.A.2001,18(7):1465–1470
[20] J.N.Mait,H.P.Herzig.Diffractive Optics and Micro-optics.J.Opt.Soc.Am.A.2001,18(11):1093–1094
[21] J.R.Leger,G.M.Morris.Diffractive Optics:An Introduction to the Feature. Appl.Opt.1993,32(14):2481–2482
[22] R.Magnusson,M.T.Gale.Diffractive Optics and Micro-optics:Introduction to the Feature Issue.Appl.Opt.2001,40(32):5817–5818
[23]林杰应用边界元方法分析微柱透镜的聚焦特性(博士学位论文)。哈尔滨工业大学2007.6
[24] Y.Arieli,S.Ozeri,T.Eisenberg,S.Noach.Design of a Diffractive Optical Element for Wide Spectral Bandwidth.Opt.Lett.1998,23(11):823–824
[25] S.Noach,Y.Arieli,T.Eisenberg.Wave-front Control and Aberration Correction with a Diffractive Optical Element.Opt.Lett.1999,24(5):333–335
[26] H.Lajunen,J.Tervo,J.Turunen.High-efficiency Broadband Diffractive Elements Based on Polarization Gratings.Opt.Lett.2004,29(8):803–805
[27] A.Hermerschmidt,S.Kru¨ger,G.Wernicke.Binary Diffractive Beam Splitters with Arbitrary Diffraction Angles.Opt.Lett.2007,32(5):448–450
[28] R.Borghi,G.Cincotti,M.Santarsiero.Diffractive Variable Beam Splitter:Optimal Design.J.Opt.Soc.Am.A.2000,17(1):63–73
[29]刘鹏利用二元光学元件实现激光波前整形(硕士学位论文)大连理工大学2008.6
[30]. R.W.Gerchberg and W.O.Saxton,”A practical algorithm for the determination of phase from image and difraction plane pietures,”Optik 35,237-246(1972)
[31]孙枭东多功能衍射光学元件的设计与分析(硕士学位论文)北京交通大学2006.12
[32]G.Z.Yang,B.Z.Dong,B.Y.Gu,J.Y.Zhuang,and O.K.Ersoy,”Gerchberg一saxton and Yang-Gu algorithms for phase retrieval in a nonunilary transform system:a comparison,”Appl.Opt.33,209-218(1994).
[33]B.Gu, G.Yang ,andB.Dong,““General theory for performing an optical transform“,Appl.Opt.25,3197-3206(1996).
[34] .G.Yang,B.Gu,X.Tan,M.P.Chang,B.Dong,and O.K.Ersoy,“Iterative optimization approach for the design of diffractive phase elements simultaneously implementing several optieal functions,”J.Opt.Soc.Am.A11 1632-1640(1994)
[35]M.A.Seldowitz,J.P.Allebach,and D.W.Sweeney,”Synthesis of digital holograms by direct binary search,”Appl.Opt.26,2788-2798(1987).
[36]S.Kirkpatrick,C.D.Gelatt,andM.P.Vecchi,”Optimization by simulated annealing,”Science 220,671-680(1983).
[37] D.E.Goldbet,Genetic algorithm in search,optimization and machine learning.(Addison-Wesley,Mass.1987)
[38]S.Kirkpatrick,C.D.Gelatt,andM.P.Vecchi,”Optimization by simulated annealing,”Science 220,671-680(1983)
[39] D.E.Goldbet,Genetic algorithm in search,optimization and machine learning.(Addison-Wesley,Mass.1987)
[40] E.N.Leith, A.Kozma, J.Upatnieks, J.Marks, N.Massey: Appl. Opt. 5, 1303 (1966)
[41] H.Kogelnik: Bell Syst. Tech. J. 48, 2909 (1969)
[42]. C.B.Burckhardt: J. Opt. Soc. Am. 56, t502 (1966)
[43]. F.G.Kaspar: J. Opt. Soc. Am. 63, 37 (1973)
[44]王二虎光折变多重体光栅写入方法及其应用研究(硕士学位论文)西北工业大学2004.3
[45]陶世荃,王大勇,江竹青,袁泉,光全息存储,北京工业大学出版社,1998,58一59.
[46]郭儒,潘士宏,体光折变栅的高阶衍射,南开大学学报,1996,29(3):75一79.
[45] M.Born, E.Wolf Principles of Optics.7th ed.Cambridge,UK,1999
[46]孙红琼计算机光学元件的特性研究(硕士学位论文)电子科技大学2007.3
[2] W. B. Veldkamp, T. J. McHugh. Binary Optics Scientific American.1992,266:92–97
[3]W. B.Veldkamp.Overview of Micro-optics:Past,Present,and Future. SPIE. 1991, 1544: 287–299
[4] J. Lcger, M.Holz, G.Swanson, W.B.Veldkamp. Coherent Laser Beam Addition:An Application of Binary Optics Technology. Lincoln Lab.J.1988,1(2):225–246
[5]金国藩,严瑛白,邬敏贤等著.二元光学.国防工业出版社,1998:9–12
[6] H.P.Herzig主编,周海宪等译.微光学元件、系统和应用.Taylor & Francis Ltd,1997:2–6
[7] J.R.Leger,M.G..Moharam,T.K. Gaylord. Diffractive Optics: An Introduction to the Feature Issue.Appl.Opt.1995,34(14):2399–2559
[8]J. A. Cox, M.G. Moharam, H. P. Herzig, J.N.Mait. Diffractive Optics and Micro-optics: Modeling, Design, Fabrication, and Applications.J.Opt.Soc..Am.A.1999,16(5):1093–1094
[9] J.M.Bendickson. Analysis of Finite Diffractive Optical Elements .Ph.D. thesis, Georgia Institute of Technology.2000
[10] J.Tervo.On Electromagnetic Treatment of Free-space Propagation and Paraxial Diffractive Optics. Ph.D. thesis, University of Joensuu.2002
[11] Y.Yirmiyahu, A.Niv,G.Biener, V.Kleiner,E.Hasman. Vectorial Vortex Mode Transformation for a Hollow Waveguide Using Pancharatnam -Berry Phase Optical Elements.Opt.Lett.2006,31(22):3252–3254
[12] G.Yang,B.Gu,X.Tan,M.Chang,B.Dong,O.K.Ersoy.Iterative Optimization Approach for the Design of Diffractive Phase Elements Simultaneously Implementing Several Optical Functions.J.Opt.Soc.Am.A.1994,11(5):1632-1640
[13] D.Feng,Y.Yan,G Jin,M.Wang.Rigorous Concept for the Analysis of Diffractive Lenses with Different Axial Resolution and High Lateral Resolution.Opt.Express.2003,11(17):1987–1994
[14] F.Di,Y.Yingbai,J.Guofan,T.Qiaofeng,H.Liu.Rigorous Electromagnetic Design of Finite-aperture Diffractive Optical Elements by Use of an Iterative Optimization Algorithm.J.Opt.Soc.Am.A.2003,20(9):1739–1746
[15] D.Feng,Y.Yan,G.Jin,S.Fan.Rigorous Electromagnetic Design of Finite aperture Diffractive Optical Elements by Use of an Iterative Optimization Algorithm.J.Opt.Soc.Am.A.2003,20(9):1739–1746
[16] S.-Q.Wang,J.Liu,B.-Y.Gu,Y.-Q.Wang,B.Hu,X.-D.Sun,S.Di.Rigorous Electromagnetic Analysis of the Common Focusing Characteristics of a Cylindrical Microlens with Long Focal Depth and under Multiwavelength Illumination.J.Opt.Soc.Am.A.2007,24(2):512–516
[17] J.Liu,B.-Y.Gu,B.-Z.Dong,G.-Z.Yang.Interference Effect of Dual Diffractive Cylindrical Microlenses Analyzed by Rigorous Electromagnetic Theory.J.Opt.Soc.Am.A.2001,18(3):526–536
[18] J.Liu,B.-Y.Gu.Laser Beam Shaping with Polarization-selective Diffractive PhaseElements.Appl.Opt.2000,39(18):3089–3092
[19] B.-Z.Dong,J.Liu,B.-Y.Gu,G.-Z.Yang,J.Wang.Rigorous Electromagnetic Analysis of a Microcylindrical Axilens with Long Focal Depth and High Transverse Resolution.J.Opt.Soc.Am.A.2001,18(7):1465–1470
[20] J.N.Mait,H.P.Herzig.Diffractive Optics and Micro-optics.J.Opt.Soc.Am.A.2001,18(11):1093–1094
[21] J.R.Leger,G.M.Morris.Diffractive Optics:An Introduction to the Feature. Appl.Opt.1993,32(14):2481–2482
[22] R.Magnusson,M.T.Gale.Diffractive Optics and Micro-optics:Introduction to the Feature Issue.Appl.Opt.2001,40(32):5817–5818
[23]林杰应用边界元方法分析微柱透镜的聚焦特性(博士学位论文)。哈尔滨工业大学2007.6
[24] Y.Arieli,S.Ozeri,T.Eisenberg,S.Noach.Design of a Diffractive Optical Element for Wide Spectral Bandwidth.Opt.Lett.1998,23(11):823–824
[25] S.Noach,Y.Arieli,T.Eisenberg.Wave-front Control and Aberration Correction with a Diffractive Optical Element.Opt.Lett.1999,24(5):333–335
[26] H.Lajunen,J.Tervo,J.Turunen.High-efficiency Broadband Diffractive Elements Based on Polarization Gratings.Opt.Lett.2004,29(8):803–805
[27] A.Hermerschmidt,S.Kru¨ger,G.Wernicke.Binary Diffractive Beam Splitters with Arbitrary Diffraction Angles.Opt.Lett.2007,32(5):448–450
[28] R.Borghi,G.Cincotti,M.Santarsiero.Diffractive Variable Beam Splitter:Optimal Design.J.Opt.Soc.Am.A.2000,17(1):63–73
[29]刘鹏利用二元光学元件实现激光波前整形(硕士学位论文)大连理工大学2008.6
[30]. R.W.Gerchberg and W.O.Saxton,”A practical algorithm for the determination of phase from image and difraction plane pietures,”Optik 35,237-246(1972)
[31]孙枭东多功能衍射光学元件的设计与分析(硕士学位论文)北京交通大学2006.12
[32]G.Z.Yang,B.Z.Dong,B.Y.Gu,J.Y.Zhuang,and O.K.Ersoy,”Gerchberg一saxton and Yang-Gu algorithms for phase retrieval in a nonunilary transform system:a comparison,”Appl.Opt.33,209-218(1994).
[33]B.Gu, G.Yang ,andB.Dong,““General theory for performing an optical transform“,Appl.Opt.25,3197-3206(1996).
[34] .G.Yang,B.Gu,X.Tan,M.P.Chang,B.Dong,and O.K.Ersoy,“Iterative optimization approach for the design of diffractive phase elements simultaneously implementing several optieal functions,”J.Opt.Soc.Am.A11 1632-1640(1994)
[35]M.A.Seldowitz,J.P.Allebach,and D.W.Sweeney,”Synthesis of digital holograms by direct binary search,”Appl.Opt.26,2788-2798(1987).
[36]S.Kirkpatrick,C.D.Gelatt,andM.P.Vecchi,”Optimization by simulated annealing,”Science 220,671-680(1983).
[37] D.E.Goldbet,Genetic algorithm in search,optimization and machine learning.(Addison-Wesley,Mass.1987)
[38]S.Kirkpatrick,C.D.Gelatt,andM.P.Vecchi,”Optimization by simulated annealing,”Science 220,671-680(1983)
[39] D.E.Goldbet,Genetic algorithm in search,optimization and machine learning.(Addison-Wesley,Mass.1987)
[40] E.N.Leith, A.Kozma, J.Upatnieks, J.Marks, N.Massey: Appl. Opt. 5, 1303 (1966)
[41] H.Kogelnik: Bell Syst. Tech. J. 48, 2909 (1969)
[42]. C.B.Burckhardt: J. Opt. Soc. Am. 56, t502 (1966)
[43]. F.G.Kaspar: J. Opt. Soc. Am. 63, 37 (1973)
[44]王二虎光折变多重体光栅写入方法及其应用研究(硕士学位论文)西北工业大学2004.3
[45]陶世荃,王大勇,江竹青,袁泉,光全息存储,北京工业大学出版社,1998,58一59.
[46]郭儒,潘士宏,体光折变栅的高阶衍射,南开大学学报,1996,29(3):75一79.
[45] M.Born, E.Wolf Principles of Optics.7th ed.Cambridge,UK,1999
[46]孙红琼计算机光学元件的特性研究(硕士学位论文)电子科技大学2007.3